internal/ceres/schur_eliminator_test.cc - ceres-solver - Git at Google

 // Ceres Solver - A fast non-linear least squares minimizer
 // Copyright 2015 Google Inc. All rights reserved.
 // http://ceres-solver.org/
 //
 // Redistribution and use in source and binary forms, with or without
 // modification, are permitted provided that the following conditions are met:
 //
 // * Redistributions of source code must retain the above copyright notice,
 //   this list of conditions and the following disclaimer.
 // * Redistributions in binary form must reproduce the above copyright notice,
 //   this list of conditions and the following disclaimer in the documentation
 //   and/or other materials provided with the distribution.
 // * Neither the name of Google Inc. nor the names of its contributors may be
 //   used to endorse or promote products derived from this software without
 //   specific prior written permission.
 //
 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
 // LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 // CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
 // SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
 // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
 // CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 // ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 // POSSIBILITY OF SUCH DAMAGE.
 //
 // Author: sameeragarwal@google.com (Sameer Agarwal)

 #include "ceres/schur_eliminator.h"

 #include <memory>
 #include "Eigen/Dense"
 #include "ceres/block_random_access_dense_matrix.h"
 #include "ceres/block_sparse_matrix.h"
 #include "ceres/casts.h"
 #include "ceres/context_impl.h"
 #include "ceres/detect_structure.h"
 #include "ceres/internal/eigen.h"
 #include "ceres/linear_least_squares_problems.h"
 #include "ceres/test_util.h"
 #include "ceres/triplet_sparse_matrix.h"
 #include "ceres/types.h"
 #include "glog/logging.h"
 #include "gtest/gtest.h"

 // TODO(sameeragarwal): Reduce the size of these tests and redo the
 // parameterization to be more efficient.

 namespace ceres {
 namespace internal {

 class SchurEliminatorTest : public ::testing::Test {
  protected:
   void SetUpFromId(int id) {
     std::unique_ptr<LinearLeastSquaresProblem>
         problem(CreateLinearLeastSquaresProblemFromId(id));
     CHECK(problem != nullptr);
     SetupHelper(problem.get());
   }

   void SetupHelper(LinearLeastSquaresProblem* problem) {
     A.reset(down_cast<BlockSparseMatrix*>(problem->A.release()));
     b.reset(problem->b.release());
     D.reset(problem->D.release());

     num_eliminate_blocks = problem->num_eliminate_blocks;
     num_eliminate_cols = 0;
     const CompressedRowBlockStructure* bs = A->block_structure();

     for (int i = 0; i < num_eliminate_blocks; ++i) {
       num_eliminate_cols += bs->cols[i].size;
     }
   }

   // Compute the golden values for the reduced linear system and the
   // solution to the linear least squares problem using dense linear
   // algebra.
   void ComputeReferenceSolution(const Vector& D) {
     Matrix J;
     A->ToDenseMatrix(&J);
     VectorRef f(b.get(), J.rows());

     Matrix H  =  (D.cwiseProduct(D)).asDiagonal();
     H.noalias() += J.transpose() * J;

     const Vector g = J.transpose() * f;
     const int schur_size = J.cols() - num_eliminate_cols;

     lhs_expected.resize(schur_size, schur_size);
     lhs_expected.setZero();

     rhs_expected.resize(schur_size);
     rhs_expected.setZero();

     sol_expected.resize(J.cols());
     sol_expected.setZero();

     Matrix P = H.block(0, 0, num_eliminate_cols, num_eliminate_cols);
     Matrix Q = H.block(0,
                        num_eliminate_cols,
                        num_eliminate_cols,
                        schur_size);
     Matrix R = H.block(num_eliminate_cols,
                        num_eliminate_cols,
                        schur_size,
                        schur_size);
     int row = 0;
     const CompressedRowBlockStructure* bs = A->block_structure();
     for (int i = 0; i < num_eliminate_blocks; ++i) {
       const int block_size =  bs->cols[i].size;
       P.block(row, row,  block_size, block_size) =
           P
           .block(row, row,  block_size, block_size)
           .llt()
           .solve(Matrix::Identity(block_size, block_size));
       row += block_size;
     }

     lhs_expected
         .triangularView<Eigen::Upper>() = R - Q.transpose() * P * Q;
     rhs_expected =
         g.tail(schur_size) - Q.transpose() * P * g.head(num_eliminate_cols);
     sol_expected = H.llt().solve(g);
   }

   void EliminateSolveAndCompare(const VectorRef& diagonal,
                                 bool use_static_structure,
                                 const double relative_tolerance) {
     const CompressedRowBlockStructure* bs = A->block_structure();
     const int num_col_blocks = bs->cols.size();
     std::vector<int> blocks(num_col_blocks - num_eliminate_blocks, 0);
     for (int i = num_eliminate_blocks; i < num_col_blocks; ++i) {
       blocks[i - num_eliminate_blocks] = bs->cols[i].size;
     }

     BlockRandomAccessDenseMatrix lhs(blocks);

     const int num_cols = A->num_cols();
     const int schur_size = lhs.num_rows();

     Vector rhs(schur_size);

     LinearSolver::Options options;
     ContextImpl context;
     options.context = &context;
     options.elimination_groups.push_back(num_eliminate_blocks);
     if (use_static_structure) {
       DetectStructure(*bs,
                       num_eliminate_blocks,
                       &options.row_block_size,
                       &options.e_block_size,
                       &options.f_block_size);
     }

     std::unique_ptr<SchurEliminatorBase> eliminator;
     eliminator.reset(SchurEliminatorBase::Create(options));
     const bool kFullRankETE = true;
     eliminator->Init(num_eliminate_blocks, kFullRankETE, A->block_structure());
     eliminator->Eliminate(A.get(), b.get(), diagonal.data(), &lhs, rhs.data());

     MatrixRef lhs_ref(lhs.mutable_values(), lhs.num_rows(), lhs.num_cols());
     Vector reduced_sol  =
         lhs_ref
         .selfadjointView<Eigen::Upper>()
         .llt()
         .solve(rhs);

     // Solution to the linear least squares problem.
     Vector sol(num_cols);
     sol.setZero();
     sol.tail(schur_size) = reduced_sol;
     eliminator->BackSubstitute(A.get(),
                                b.get(),
                                diagonal.data(),
                                reduced_sol.data(),
                                sol.data());

     Matrix delta = (lhs_ref - lhs_expected).selfadjointView<Eigen::Upper>();
     double diff = delta.norm();
     EXPECT_NEAR(diff / lhs_expected.norm(), 0.0, relative_tolerance);
     EXPECT_NEAR((rhs - rhs_expected).norm() / rhs_expected.norm(), 0.0,
                 relative_tolerance);
     EXPECT_NEAR((sol - sol_expected).norm() / sol_expected.norm(), 0.0,
                 relative_tolerance);
   }

   std::unique_ptr<BlockSparseMatrix> A;
   std::unique_ptr<double[]> b;
   std::unique_ptr<double[]> D;
   int num_eliminate_blocks;
   int num_eliminate_cols;

   Matrix lhs_expected;
   Vector rhs_expected;
   Vector sol_expected;
 };

 TEST_F(SchurEliminatorTest, ScalarProblemNoRegularization) {
   SetUpFromId(2);
   Vector zero(A->num_cols());
   zero.setZero();

   ComputeReferenceSolution(VectorRef(zero.data(), A->num_cols()));
   EliminateSolveAndCompare(VectorRef(zero.data(), A->num_cols()), true, 1e-14);
   EliminateSolveAndCompare(VectorRef(zero.data(), A->num_cols()), false, 1e-14);
 }

 TEST_F(SchurEliminatorTest, ScalarProblemWithRegularization) {
   SetUpFromId(2);
   ComputeReferenceSolution(VectorRef(D.get(), A->num_cols()));
   EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), true, 1e-14);
   EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), false, 1e-14);
 }

 TEST_F(SchurEliminatorTest, VaryingFBlockSizeWithStaticStructure) {
   SetUpFromId(4);
   ComputeReferenceSolution(VectorRef(D.get(), A->num_cols()));
   EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), true, 1e-14);
 }

 TEST_F(SchurEliminatorTest, VaryingFBlockSizeWithoutStaticStructure) {
   SetUpFromId(4);
   ComputeReferenceSolution(VectorRef(D.get(), A->num_cols()));
   EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), false, 1e-14);
 }

 }  // namespace internal
 }  // namespace ceres
	// Ceres Solver - A fast non-linear least squares minimizer
	// Copyright 2015 Google Inc. All rights reserved.
	// http://ceres-solver.org/
	//
	// Redistribution and use in source and binary forms, with or without
	// modification, are permitted provided that the following conditions are met:
	//
	// * Redistributions of source code must retain the above copyright notice,
	// this list of conditions and the following disclaimer.
	// * Redistributions in binary form must reproduce the above copyright notice,
	// this list of conditions and the following disclaimer in the documentation
	// and/or other materials provided with the distribution.
	// * Neither the name of Google Inc. nor the names of its contributors may be
	// used to endorse or promote products derived from this software without
	// specific prior written permission.
	//
	// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
	// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
	// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
	// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
	// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
	// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
	// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
	// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
	// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
	// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
	// POSSIBILITY OF SUCH DAMAGE.
	//
	// Author: sameeragarwal@google.com (Sameer Agarwal)

	#include "ceres/schur_eliminator.h"

	#include <memory>
	#include "Eigen/Dense"
	#include "ceres/block_random_access_dense_matrix.h"
	#include "ceres/block_sparse_matrix.h"
	#include "ceres/casts.h"
	#include "ceres/context_impl.h"
	#include "ceres/detect_structure.h"
	#include "ceres/internal/eigen.h"
	#include "ceres/linear_least_squares_problems.h"
	#include "ceres/test_util.h"
	#include "ceres/triplet_sparse_matrix.h"
	#include "ceres/types.h"
	#include "glog/logging.h"
	#include "gtest/gtest.h"

	// TODO(sameeragarwal): Reduce the size of these tests and redo the
	// parameterization to be more efficient.

	namespace ceres {
	namespace internal {

	class SchurEliminatorTest : public ::testing::Test {
	protected:
	void SetUpFromId(int id) {
	std::unique_ptr<LinearLeastSquaresProblem>
	problem(CreateLinearLeastSquaresProblemFromId(id));
	CHECK(problem != nullptr);
	SetupHelper(problem.get());
	}

	void SetupHelper(LinearLeastSquaresProblem* problem) {
	A.reset(down_cast<BlockSparseMatrix*>(problem->A.release()));
	b.reset(problem->b.release());
	D.reset(problem->D.release());

	num_eliminate_blocks = problem->num_eliminate_blocks;
	num_eliminate_cols = 0;
	const CompressedRowBlockStructure* bs = A->block_structure();

	for (int i = 0; i < num_eliminate_blocks; ++i) {
	num_eliminate_cols += bs->cols[i].size;
	}
	}

	// Compute the golden values for the reduced linear system and the
	// solution to the linear least squares problem using dense linear
	// algebra.
	void ComputeReferenceSolution(const Vector& D) {
	Matrix J;
	A->ToDenseMatrix(&J);
	VectorRef f(b.get(), J.rows());

	Matrix H = (D.cwiseProduct(D)).asDiagonal();
	H.noalias() += J.transpose() * J;

	const Vector g = J.transpose() * f;
	const int schur_size = J.cols() - num_eliminate_cols;

	lhs_expected.resize(schur_size, schur_size);
	lhs_expected.setZero();

	rhs_expected.resize(schur_size);
	rhs_expected.setZero();

	sol_expected.resize(J.cols());
	sol_expected.setZero();

	Matrix P = H.block(0, 0, num_eliminate_cols, num_eliminate_cols);
	Matrix Q = H.block(0,
	num_eliminate_cols,
	num_eliminate_cols,
	schur_size);
	Matrix R = H.block(num_eliminate_cols,
	num_eliminate_cols,
	schur_size,
	schur_size);
	int row = 0;
	const CompressedRowBlockStructure* bs = A->block_structure();
	for (int i = 0; i < num_eliminate_blocks; ++i) {
	const int block_size = bs->cols[i].size;
	P.block(row, row, block_size, block_size) =
	P
	.block(row, row, block_size, block_size)
	.llt()
	.solve(Matrix::Identity(block_size, block_size));
	row += block_size;
	}

	lhs_expected
	.triangularView<Eigen::Upper>() = R - Q.transpose() * P * Q;
	rhs_expected =
	g.tail(schur_size) - Q.transpose() * P * g.head(num_eliminate_cols);
	sol_expected = H.llt().solve(g);
	}

	void EliminateSolveAndCompare(const VectorRef& diagonal,
	bool use_static_structure,
	const double relative_tolerance) {
	const CompressedRowBlockStructure* bs = A->block_structure();
	const int num_col_blocks = bs->cols.size();
	std::vector<int> blocks(num_col_blocks - num_eliminate_blocks, 0);
	for (int i = num_eliminate_blocks; i < num_col_blocks; ++i) {
	blocks[i - num_eliminate_blocks] = bs->cols[i].size;
	}

	BlockRandomAccessDenseMatrix lhs(blocks);

	const int num_cols = A->num_cols();
	const int schur_size = lhs.num_rows();

	Vector rhs(schur_size);

	LinearSolver::Options options;
	ContextImpl context;
	options.context = &context;
	options.elimination_groups.push_back(num_eliminate_blocks);
	if (use_static_structure) {
	DetectStructure(*bs,
	num_eliminate_blocks,
	&options.row_block_size,
	&options.e_block_size,
	&options.f_block_size);
	}

	std::unique_ptr<SchurEliminatorBase> eliminator;
	eliminator.reset(SchurEliminatorBase::Create(options));
	const bool kFullRankETE = true;
	eliminator->Init(num_eliminate_blocks, kFullRankETE, A->block_structure());
	eliminator->Eliminate(A.get(), b.get(), diagonal.data(), &lhs, rhs.data());

	MatrixRef lhs_ref(lhs.mutable_values(), lhs.num_rows(), lhs.num_cols());
	Vector reduced_sol =
	lhs_ref
	.selfadjointView<Eigen::Upper>()
	.llt()
	.solve(rhs);

	// Solution to the linear least squares problem.
	Vector sol(num_cols);
	sol.setZero();
	sol.tail(schur_size) = reduced_sol;
	eliminator->BackSubstitute(A.get(),
	b.get(),
	diagonal.data(),
	reduced_sol.data(),
	sol.data());

	Matrix delta = (lhs_ref - lhs_expected).selfadjointView<Eigen::Upper>();
	double diff = delta.norm();
	EXPECT_NEAR(diff / lhs_expected.norm(), 0.0, relative_tolerance);
	EXPECT_NEAR((rhs - rhs_expected).norm() / rhs_expected.norm(), 0.0,
	relative_tolerance);
	EXPECT_NEAR((sol - sol_expected).norm() / sol_expected.norm(), 0.0,
	relative_tolerance);
	}

	std::unique_ptr<BlockSparseMatrix> A;
	std::unique_ptr<double[]> b;
	std::unique_ptr<double[]> D;
	int num_eliminate_blocks;
	int num_eliminate_cols;

	Matrix lhs_expected;
	Vector rhs_expected;
	Vector sol_expected;
	};

	TEST_F(SchurEliminatorTest, ScalarProblemNoRegularization) {
	SetUpFromId(2);
	Vector zero(A->num_cols());
	zero.setZero();

	ComputeReferenceSolution(VectorRef(zero.data(), A->num_cols()));
	EliminateSolveAndCompare(VectorRef(zero.data(), A->num_cols()), true, 1e-14);
	EliminateSolveAndCompare(VectorRef(zero.data(), A->num_cols()), false, 1e-14);
	}

	TEST_F(SchurEliminatorTest, ScalarProblemWithRegularization) {
	SetUpFromId(2);
	ComputeReferenceSolution(VectorRef(D.get(), A->num_cols()));
	EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), true, 1e-14);
	EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), false, 1e-14);
	}

	TEST_F(SchurEliminatorTest, VaryingFBlockSizeWithStaticStructure) {
	SetUpFromId(4);
	ComputeReferenceSolution(VectorRef(D.get(), A->num_cols()));
	EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), true, 1e-14);
	}

	TEST_F(SchurEliminatorTest, VaryingFBlockSizeWithoutStaticStructure) {
	SetUpFromId(4);
	ComputeReferenceSolution(VectorRef(D.get(), A->num_cols()));
	EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), false, 1e-14);
	}

	} // namespace internal
	} // namespace ceres